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Elementary Abelian $$p$$-groups of rank $$2p+3$$ are not CI-groups. (English) Zbl 1294.20069
Summary: For every prime $$p>2$$ we exhibit a Cayley graph on $$\mathbb Z_p^{2p+3}$$ which is not a CI-graph. This proves that an elementary Abelian $$p$$-group of rank greater than or equal to $$2p+3$$ is not a CI-group. The proof is elementary and uses only multivariate polynomials and basic tools of linear algebra. Moreover, we apply our technique to give a uniform explanation for the recent works of Muzychuk and Spiga concerning the problem.
Reviewer: Reviewer (Berlin)

##### MSC:
 20K01 Finite abelian groups 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
##### Keywords:
Cayley graphs; CI-groups; elementary Abelian $$p$$-groups
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##### References:
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